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Pseudoconvex function information


In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. The property must hold in all of the function domain, and not only for nearby points.

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Pseudoconvex function

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variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima...

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Pseudoconvexity

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theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets...

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Convex function

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inequality Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF). www.stat...

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Invex function

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E-invex functions were introduced by Abdulaleem as a generalization of differentiable convex functions. Convex function Pseudoconvex function Quasiconvex...

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Quasiconvex function

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quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense...

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Plurisubharmonic function

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constant. In several complex variables, plurisubharmonic functions are used to describe pseudoconvex domains, domains of holomorphy and Stein manifolds. The...

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Function of several complex variables

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subharmonic function looks like a kind of convex function, so it was named by Levi as a pseudoconvex domain (Hartogs's pseudoconvexity). Pseudoconvex domain...

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Analytic function

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leads to the notion of pseudoconvexity. Cauchy–Riemann equations Holomorphic function Paley–Wiener theorem Quasi-analytic function Infinite compositions...

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List of numerical analysis topics

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method Convex analysis — function f such that f(tx + (1 − t)y) ≥ tf(x) + (1 − t)f(y) for t ∈ [0,1] Pseudoconvex functionfunction f such that ∇f · (y −...

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Stein manifold

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strongly pseudoconvex manifold. The latter means that it has a strongly pseudoconvex (or plurisubharmonic) exhaustive function, i.e. a smooth real function ψ...

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Domain of holomorphy

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problem. Behnke–Stein theorem Levi pseudoconvex solution of the Levi problem Stein manifold Steven G. Krantz. Function Theory of Several Complex Variables...

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CR manifold

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and only if it is (strictly) pseudoconvex as a CR manifold from the side of the domain. (See plurisubharmonic functions and Stein manifold.) An abstract...

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Complex convexity

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and the plurisubharmonic functions. Geometrically, these classes of functions correspond to convex domains and pseudoconvex domains, but there are also...

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Stochastic gradient descent

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converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum...

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Convex set

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theorem Holomorphically convex hull Integrally-convex set John ellipsoid Pseudoconvexity Radon's theorem Shapley–Folkman lemma Symmetric set Morris, Carla C...

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Charles Fefferman

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study of the asymptotics of the Bergman kernel off the boundaries of pseudoconvex domains in C n {\displaystyle \mathbb {C} ^{n}} . He has studied mathematical...

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David Catlin

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under Joseph Kohn with thesis Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains. He is a professor at Purdue University. He solved...

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Eugenio Elia Levi

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a special case. In the theory of functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the...

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Nessim Sibony

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1990 he was an Invited Speaker with talk Some recent results on weakly pseudoconvex domains at the ICM in Kyōto. He was a senior member of the Institut Universitaire...

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Louis Nirenberg

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Kohn, following earlier work by Kohn, studied the ∂-Neumann problem on pseudoconvex domains, and demonstrated the relation of the regularity theory to the...

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Galia Dafni

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her Ph.D. in 1993. Her doctoral dissertation, Hardy Spaces on Strongly Pseudoconvex Domains in C n {\displaystyle C^{n}} and Domains of Finite Type in C...

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Alexander Nagel

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the ∂ ¯ {\displaystyle {\overline {\partial }}} -Neumann problem in pseudoconvex domains of finite type in C {\displaystyle \mathbb {C} } 2 ". Acta Mathematica...

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Kengo Hirachi

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of Mathematics (2000) Hirachi constructed CR invariants of strongly pseudoconvex boundaries via a deep study of the logarithmic singularity of the Bergman...

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